Thus, there are a number of different possible scales on which to define non-interaction; while the biologist may prefer the log-complement scale because of the natural interpretability of probabilistic independence, the epidemiologist has traditionally preferred the log-odds scale. In practice, this distinction may not be a subtle one. For example, suppose the background risk (i.e. the risk in those with neither A nor B) is 10 per 100,000, while the risk with A alone is 20 per 100,000 and the risk with B alone is 30 per 100,000. Then if the risk in those with both is 50 per 100,000 there is antagonism (competition?) between A and B under a log-odds null, but synergism (enhancement?) under a log-complement null, because the expectation under the former is 60 per 100,000, versus 40 per 100,000 under the latter. Thus, under one model the two exposures mutually enhance each other and under the other they are seen as working against each other. So the direction of the finding can be different, depending on the selected model for nonindependence. Another consideration is that power
